Problem: Simplify the following expression: $\dfrac{18t^5}{42t}$ You can assume $t \neq 0$.
Solution: $ \dfrac{18t^5}{42t} = \dfrac{18}{42} \cdot \dfrac{t^5}{t} $ To simplify $\frac{18}{42}$ , find the greatest common factor (GCD) of $18$ and $42$ $18 = 2 \cdot 3 \cdot 3$ $42 = 2 \cdot 3 \cdot 7$ $ \mbox{GCD}(18, 42) = 2 \cdot 3 = 6 $ $ \dfrac{18}{42} \cdot \dfrac{t^5}{t} = \dfrac{6 \cdot 3}{6 \cdot 7} \cdot \dfrac{t^5}{t} $ $\phantom{ \dfrac{18}{42} \cdot \dfrac{5}{1}} = \dfrac{3}{7} \cdot \dfrac{t^5}{t} $ $ \dfrac{t^5}{t} = \dfrac{t \cdot t \cdot t \cdot t \cdot t}{t} = t^4 $ $ \dfrac{3}{7} \cdot t^4 = \dfrac{3t^4}{7} $